Polarization phase relationships via multiple Morse wavelets. II. Data analysis

• Published in: Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 459; no. 2031; pp. 641 - 657
• Main Authors: Olhede, S., Walden, A. T.
• Format: Journal Article
• Language: English
• Published: The Royal Society 08-03-2003
• Subjects: Earthquake; Earthquakes; Eigenvalues; Eigenvectors; Estimate reliability; Fast Fourier transformations; Interplanetary shock waves; Love waves; Multiple Wavelets; Phase; Polarization Solar Magnetic Field; Signal noise; Solar magnetic field; Three-Component Signals; Time series
• ISSN: 1364-5021; 1471-2946
• DOI: 10.1098/rspa.2002.1050

Three examples are provided of the use of multiple generalized Morse wavelets for polarization analysis of three-component recordings where phase relationships between components of the signal are transient. The example three-component signals are (i) synthetic, (ii) the radial, transverse and vertical components of an earthquake, and (iii) the radial, transverse and normal components of the solar magnetic field measured by the Ulysses spacecraft upstream of an interplanetary shock. Working in the scale-time plane (a,b), the multiple-wavelet approach detects coherent motion with elliptical polarization in all three cases. Our graphical presentations fully take into account restrictions imposed by two factors: the minimum usable scale, and wraparound effects caused by Fourier transform computations, and consequently a maximum usable scale.